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A young man called Enrico Fabris won the 1,500m speed skating in Turin this week, and Italy’s fourth gold medal of the 2006 Winter Olympics. He was roared on – according to a press report that must have appeared in dozens of newspapers round the world – by a “rabid” crowd.

Rabies! That, on top of the bird flu! In fact, from my seat in the arena, tepid seemed a better word than rabid. I have never seen a home country gold medal greeted with such restraint; and throughout the event, Fabris’s supporters were outnumbered and outshouted by hundreds of orange-clad Dutchmen.

There is perhaps an element of racial stereotyping here: Italians, fans, Mediterranean, rabid. Most Italians might see it differently and more accurately: the Torinese, spectators, northerly, cool and off-handed.

And indeed Turin 2006 will probably go down as the most off-hand games of recent times, perhaps since Paris 1900, when many of the athletes never even knew they were at the Olympics. There may be less visual display in the city than there is in London with six years to go. Ticket sales have never been hot. And even the local sporting press has found it hard to take its eyes off the football.

Turin, the story goes, never wanted to host the games but thought there might be some PR mileage in bidding. It fell their way through the vagaries of International Olympic Committee politics and both sides have had some years of regret. “My sense is that these games came closer to falling apart than either Athens or Atlanta,” said one IOC source. “No one took into account all the disconnects you get in Italy. Rome wasn’t talking to the region. The region wasn’t talking to the city. There wasn’t enough money and no one cared.”

But somehow on these occasions everyone does seem to muddle through. And Turin 2006 has not been without its successes: the city is lovely; the nightly medals ceremony in the Piazza Castello has provided terrific theatre (although the medals themselves, with holes in the middle, are absurd); and the snowboarding has been a triumph. But watching, say, the biathlon, with a few dozen enthusiasts standing around, you have to pinch yourself to remember this is not a school sports day.

If these Olympics have not really captured the host city’s imagination, they have certainly struggled to engage the planet. But that’s nothing to do with Turin and everything to do with the winter games as a concept. In the global scheme of things, the summer Olympics really do matter, and not just for sport. Imagine if Beijing 2008 happens to coincide with the moment when the grievances of the Chinese people reach a critical mass. Phew!

The Winter Olympics, in contrast, exist primarily as a shop window for the skiing industry. The images of taut young athletes in skintight gear perched at the top of ski runs with a background of blue sky, white snow and jagged peaks are not just part of the show; they are the thing itself. The object is to sell the local resorts as holiday venues, which poses a problem when – as was true in the first week – there isn’t actually much snow. To create a vague impression of Olympic-style breadth, a bizarre coalition of sports has been assembled, many of which would never remotely get close to a summer games. Curling (an agreeable and cerebral pastime for those of us who find lawn bowls too exciting) is only widespread in Canada and Scotland; Finland has reached the men’s final although, according to one team member, the country has only 15 serious players.

In fact, pretty much every possible sport involving ice or snow is now in the winter games except the snowball-putt, synchronised snowman-building and whatever it is Finns do after saunas with birch twigs.

The overall constituency is not global either (and climate change might shrink it further). Twenty-five countries had won medals as of yesterday morning. Of these, 19 are in Europe. In fact, the only country on the honours board south of the US and China is Australia, whose sole gold went to a curious 21-year-old self-proclaimed internet millionaire who lives in . . . Vancouver.

Notionally, 85 countries are represented in Turin. But this includes the Thai team (a 48-year-old cross-country skier), Costa Rica (a 49-year-old downhill skier), and Venezuela (a 52-year-old who did not fall off and thus avoided last place in the luge).

Given how po-faced Beijing 2008 is likely to be, we should be grateful that the spirit of Eddie the Eagle still survives. But the most telling of Winter Olympic statistics is this one: the American speed skater Shani Davis, gold medallist in the 1,000m, was said to be only the third black athlete in the 82-year history of the Winter Olympics to win any kind of medal. It’s not just the snow that’s white.